A Chance-Constrained Optimal Design of Volt/VAR Control Rules for Distributed Energy Resources

TL;DR

This paper presents a novel method for designing Volt/VAR control rules for distributed energy resources that minimizes losses while ensuring voltage stability under uncertainty, using a deep learning surrogate model for efficient optimization.

Contribution

It introduces a chance-constrained optimal design framework utilizing a recursive neural network surrogate to efficiently optimize piecewise-affine Volt/VAR rules under uncertainty.

Findings

The proposed method effectively reduces line losses.

It maintains voltage within limits despite load uncertainties.

The RNN surrogate accelerates the optimization process.

Abstract

Deciding setpoints for distributed energy resources (DERs) via local control rules rather than centralized optimization offers significant autonomy. The IEEE Standard 1547 recommends deciding DER setpoints using Volt/VAR rules. Although such rules are specified as non-increasing piecewise-affine, their exact shape is left for the utility operators to decide and possibly customize per bus and grid conditions. To address this need, this work optimally designs Volt/VAR rules to minimize ohmic losses on lines while maintaining voltages within allowable limits. This is practically relevant as excessive reactive injections could reduce equipment's lifetime due to overloading. We consider a linearized single-phase grid model. Even under this setting, optimal rule design (ORD) is technically challenging as Volt/VAR rules entail mixed-integer models, stability implications, and uncertainties in grid loading. Uncertainty is handled by minimizing the average losses under voltage chance constraints. To cope with the piecewise-affine shape of the rules, we build upon our previous reformulation of ORD as a deep learning task. A recursive neural network (RNN) surrogates Volt/VAR dynamics and thanks to back-propagation, we expedite this chance-constrained ORD. RNN weights coincide with rule parameters, and are trained using primal-dual decomposition. Numerical tests corroborate the efficacy of this novel ORD formulation and solution methodology.